Average Error: 0.0 → 0.0
Time: 8.3s
Precision: 64
\[\left(\frac{x}{2} + y \cdot x\right) + z\]
↓
\[x \cdot \left(y + 0.5\right) + z\]
\left(\frac{x}{2} + y \cdot x\right) + z
↓
x \cdot \left(y + 0.5\right) + z
double f(double x, double y, double z) {
        double r220143 = x;
        double r220144 = 2.0;
        double r220145 = r220143 / r220144;
        double r220146 = y;
        double r220147 = r220146 * r220143;
        double r220148 = r220145 + r220147;
        double r220149 = z;
        double r220150 = r220148 + r220149;
        return r220150;
}
↓
double f(double x, double y, double z) {
        double r220151 = x;
        double r220152 = y;
        double r220153 = 0.5;
        double r220154 = r220152 + r220153;
        double r220155 = r220151 * r220154;
        double r220156 = z;
        double r220157 = r220155 + r220156;
        return r220157;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(\frac{x}{2} + y \cdot x\right) + z\]

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{0.5 \cdot x + \left(z + x \cdot y\right)}\]

  3. Simplified0.0

    \[\leadsto \color{blue}{x \cdot \left(y + 0.5\right) + z}\]

  4. Final simplification0.0

    \[\leadsto x \cdot \left(y + 0.5\right) + z\]

Reproduce

herbie shell --seed 2019298 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))